On Wed, 9 Aug 1995, Ray Cromwell wrote:
> Nathan Zook wrote:
> > > don't have a GNU ftp site to hand.
> > >
> > > There's a function
> > >
> > > int mpz_probab_prime_p(mpnum, SURETY)
> > >
> > > which returns true if the prime passes SURETY probablistic prime tests.
> > >
> > > I think if it passes say 25 tests, then there will be less than a
> > > 1/2^25 chance that it is not prime.
> > >
> > > Also, on:
> > >
> > > http://dcs.ex.ac.uk/~aba/rsa-keygen.html
> > >
> >
> > The proper thing to do is to then search for a number which demonstrates
> > p is prime....
>
> And how do you do this? I'm not aware of any deterministic primality
> test which isn't atleast as hard as factoring. P-1 factorial is such
> a number which could demonstrate P is prime (compute the gcd, check if
> they are relatively prime). Good luck computing it.
>
> -Ray
Common, Ray! floor(sqrt(p))! would work fine.... ;-) Seriously, at
least 1/4 of the numbers between can p and 0 prove that p is prime. So you
try for a while. If you don't get it, you can flip back.
I apologize for being so vague. I don't have the paper I read a couple
years ago in front of me. You might contact your local math department &
ask...
Nathan